Statistical Distributions of the Volatility Index

VIX related products (ETNs, futures and options) are becoming popular financial instruments, for both hedging and speculation, these days.  The volatility index VIX was developed in the early 90’s. In its early days, it led the derivative markets. Today the dynamics has changed.  Now there is strong evidence that the VIX futures market leads the cash index.

In this post we are going to look at some statistical properties of the spot VIX index. We used data from January 1990 to May 2017. Graph below shows the kernel distribution of spot VIX.

volatility trading strategies: VIX distribution is not normal
Kernel distribution of the spot VIX index

It can be seen that the distribution of spot VIX is not normal, and it possesses a right tail.

We next look at the Q-Q plot of spot VIX. Graph below shows the Q-Q plot. It’s apparent that the distribution of spot VIX is not normal. The right-tail behavior can also be seen clearly. Intuitively, it makes sense since the VIX index often experiences very sharp, upward spikes.

volatility arbitrage: Q-Q plot of spot volatility index
Q-Q plot of spot VIX vs. standard normal

It is interesting to observe that there exists a natural floor around 9% on the left side, i.e. historically speaking, 9% has been a minimum for spot VIX.

We now look at the distribution of VIX returns. Graph below shows the Q-Q plot of VIX returns. We observe that the return distribution is closer to normal than the spot VIX distribution. However, it still exhibits the right tail behavior.

Relative value arbitrage: distribution of VIX returns
Q-Q plot of VIX returns vs. standard normal

It’s interesting to see that in the return space, the VIX distribution has a left tail similar to the equity indices. This is probably due to large decreases in the spot VIX after sharp volatility spikes.

The natural floor of the spot VIX index and its left tail in the return space can lead to construction of good risk/reward trading strategies.

UPDATE: we plotted probability mass function of spot VIX on the log scale. Graph below shows that spot VIX spent most of its time in the 12%-22% (log(VIX)=2.5 to 3.1) region during the sample period.

options trading strategies: distribution of the volatility index
Kernel distribution on the log scale

Are Short Out-of-the-Money Put Options Risky? Part 2: Dynamic Case

This post is the continuation of the previous one on the riskiness of OTM vs. ATM short put options and the effect of leverage on the risk measures. In this installment we’re going to perform similar studies with the only exception that from inception until maturity the short options are dynamically hedged. The simulation methodology and parameters are the same as in the previous study.

As a reference, results for the static case are replicated here:

ATM  (K=100)   OTM (K=90)
Margin Return Variance VaR Return Variance VaR
100% 0.0171 0.0075 0.1940 0.0118 0.0031 0.1303
50% 0.0370 0.0292 0.3844 0.0206 0.0133 0.2783
15% 0.1317 0.3155 1.2589 0.0679 0.1502 0.9339

 

Table below summarizes the results for the dynamically hedged case

ATM  (K=100)   OTM (K=90)
Margin Return Variance VaR Return Variance VaR
100% -0.0100 1.9171E-05 0.0073 -0.0059 1.4510E-05 0.0062
50% -0.0199 7.6201E-05 0.0145 -0.0118 5.8016E-05 0.0121
15% -0.0660 8.7943E-04 0.0480 -0.0400 6.5201E-04 0.0424

 

From the Table above, we observe that:

  • Similar to the static case, delta-hedged OTM put options are less risky than the ATM counterparts. However, the reduction in risk is less significant. This is probably due to the fact that delta hedging itself already reduces the risks considerably (see below).
  • Leverage also increases risks.

It is important to note that given the same notional amount, a delta-hedged position is less risky than a static position. For example, the VaR of a static, cash-secured (m=100%) short put position is 0.194, while the VaR of the corresponding dynamically-hedged position is only 0.0073. This explains why proprietary trading firms and hedge funds often engage in the practice of dynamic hedging.

Finally, we note that while Value at Risk takes into account the tail risks to some degree, it’s probably not the best measure of tail risks. Using other risk measures that better incorporate the tail risks can alter the results and lead to different conclusions.

 

Are Short Out-of-the-Money Put Options Risky?

Traders often debate whether short out-of-the-money (OTM) or at-the-money (ATM) puts are riskier. The argument for OTM put options being riskier is that their Speeds (or dGamma/dspot) are higher than the ATMs’ ones, thus the Gamma, which is negative, can increase (in absolute value) substantially during a market downturn.

In this post, we will quantify and compare the risks of short OTM and ATM put options. We do so by performing Monte Carlo simulations and calculating the Value at Risk (VaR at 95% confidence interval) and variance of the return distribution.  This strategy involves shorting unhedged puts. The return is determined as follows,

short put option

where Pt0 and PT denote the put prices at time zero and expiration respectively

K is the strike price; K=90, 100 for OTM and ATM options, respectively

m is a factor for margin.   m=100% means that we sell a cash-secured put.

Note that the above equation takes into account the margin requirement in an approximate way. The exact formula for margin calculation depends on brokers, exchanges and countries. But we believe that using a more realistic margin calculation formula will not change the conclusion of this article.

We use the same simulation methodology and parameters as in the previous post. The parameters are as follows,

Parameter Value
Initial stock price 100
Volatility 20%
Risk-free rate 0.02
Drift 0.07
Days in simulation 252
Time step (day) 1d
Number of paths 10000
Model GBM

It’s important to note that we focus here on the risks only.  Hence we utilize the same values for the option’s implied volatility and the underlying’s realized volatility. In real life the puts implied volatilities are usually higher than the realized due to volatility and skew risk premia.  This means that the strategy’s real-life expected return is normally higher.  Our simulated return is more conservative.

The table below summarizes the risk characteristics of short put options.

ATM  (K=100)   OTM (K=90)
Leverage Return Variance VaR Return Variance VaR
100% 0.0171 0.0075 0.1940 0.0118 0.0031 0.1303
50% 0.0370 0.0292 0.3844 0.0206 0.0133 0.2783
15% 0.1317 0.3155 1.2589 0.0679 0.1502 0.9339

We observe that for the same level of leverage, short OTM put positions are actually less risky than the ATM ones. For example, for m=100%, i.e. a cash-secured short put position, the variance and VaR of the OTM position are  0.0031 and 0.1303 respectively; they are smaller than the ATM option’s counterparts which are 0.0075 and 0.1940, respectively.

The risk comes from leverage. Let’s say, for example, a trader wants to sell OTM puts. Since he receives less premium for each put sold, he will likely increase the position size. For example, if he sells 2 OTM puts using leverage (m=50%), then the variance and VaR of his position are 0.0133 and 0.2783 respectively. Compared to selling 1 ATM cash-secured put, the risks increased substantially (VaR went from 0.194 to 0.2783)

In summary, ceteris paribus, a short OTM put option position is less risky than the ATM one. The danger arises when traders use excessive leverage.

Using a Market Timing Rule to Size an Option Position, A Static Case

In the previous installment, we discussed the use of a popular asset allocation/market timing rule (10M SMA rule hereafter) to size a short option position. The strategy did not work well as it was the case in traditional asset allocation. We thought that the poor performance was due to the fact that the 10M SMA rule is more of a market direction indicator that is not directly related to the PnL driver of a delta hedged position.

Recall that an option position can be loosely divided into 2 categories:  dynamic and static [1]

1-Dynamic:  the option position is delta hedged dynamically; its PnL driver is the implied/realized volatility dynamics. The profit and loss at the option expiration depends on the volatility dynamics, but not on the terminal value of the spot price.

2-Static: the option position is left unhedged; the payoff of the strategy depends on the spot price at option expiration but not on the volatility dynamics, i.e. it’s path independent.

In this post, we will apply the 10M SMA rule to a static, unhedged position. All other parameters and rules are the same as in our previous post. Briefly, the trading rules are as follows

1-NoTiming: Sell 1-Month at-the-money (ATM) put option, no rehedge.

2-10M-SMA: we only sell an ATM put option if the closing price of the underlying is greater than its 10M SMA.

Our rationale for investigating this case is that because the payoff of a static, unhedged position depends largely on the direction of the market, the 10M SMA timing rule will have a higher chance of success.

Table below summarizes and compares results of the short put strategy with and without the application of the 10M SMA rule

Strategy NoTiming 10M-SMA
Number of Trades: 115 81
Percent Winners: 0.77 0.77
Average P&L: 65.69 62.77
Largest losing trade -2702.50 -1601.00
Largest winning trade 652.00 451.50
Profit Factor (W/L): 1.47 1.54
Worst drawdown -5002.50 -1897.00

 

Graph below shows the equity curves of the 2 strategies

options trading strategies using market timing

As we can see from the Table and Graph, the 10M SMA rule performed better in this case. Although the win percentage and average PnL per trade remained approximately the same, the risks have been reduced significantly. The largest loss was reduced from $2.7K to $1.6K; drawdown decreased from $5K to $1.9K. As a result, the profit factor increased from 1.47 to 1.54.

In conclusion, the 10M SMA rule performs well in the case of a static, unhedged short put position. Using this rule, the risk-adjusted return of the trade was enhanced significantly.

 

Other related studies:

  • While researching the literature on this subject, I came across a similar study presented by E. Sinclair [2]. He showed that, for a delta hedged short strangle position, market timing based on the VIX index improved the results significantly. Since the VIX is a measure of volatility, its good performance is consistent with our understanding that for a delta hedged position, we should use a market timing indicator based on volatility and not on direction.
  • Pavel Bambásek also published similar studies recently. He used 200-Days SMA to time the market: http://www.bluetrader.cz/delta-hedging-ano-ne/

 

References

[1]  N.N. Taleb, Dynamic Hedging: Managing Vanilla and Exotic Options, Wiley, 1997

[2] E. Sinclair, Volatility Trading, Wiley, 2nd edition, 2013

Is Volatility of Volatility Increasing?

Last Wednesday, the SP500 index went down by just -1.8%, but in the volatility space it felt like the world was going to end; the volatility term structure, as measured by the VIX/VXV ratio, reached 1, i.e. the threshold where it passes from the contango to backwardation state. The near inversion of the volatility term structure can also be seen on the VIX futures curve (although to a lesser degree), as shown below.

VIX futures as at May 16 (blue line) and May 17 2017 (black line). Source: Vixcentral.com

With only -1.8% change in the underlying SPX, the associated spot VIX went from 10.65 to 15.59, a disproportional increase of 46%. The large changes in the spot and VIX futures were also reflected in the prices of VIX ETNs. For example, SVXY went down by about 18%, i.e. 9 times bigger than the SPX return. We note that in normal times SVXY has a beta of about 3-4 (as referenced to SPY).

So was the spike in volatility normal and what happened exactly?

To answer these questions, we first looked at the daily percentage changes of the VIX as a function of SPX returns. The Figure below plots the VIX changes v.s.  SPX daily returns. Note that we plotted only days in which the underlying SPX decreased more than 1.5% from the previous day’s close. The arrow points to the data point of last Wednesday.

Daily VIX changes v.s. SPX returns

A cursory look at the graph can tell us that it’s rare that a small change in the underlying SPX caused a big percentage change in the VIX.

To quantify the probability, we counted the number of occurrences when the daily SPX returns are between -2.5% and -1.5%, but the VIX index experienced an increase of 30% or greater. The data set is from January 1990 to May 19 2017, and the total sample size is 6900.

There are only 11 occurrences, which means that volatility spikes like the one of last Wednesday occurred only about 0.16% of the time. So indeed, such an event is a rare occurrence.

Table below presents the dates and VIX changes on those 11 occurrences.

Date VIX change
23/07/1990 0.515
03/08/1990 0.4068
19/08/1991 0.3235
04/02/1994 0.4186
30/05/2006 0.3086
27/04/2010 0.3057
25/02/2013 0.3402
15/04/2013 0.432
29/06/2015 0.3445
09/09/2016 0.3989
17/05/2017 0.4638

 

But what happened and what caused the VIX to go up that much?

While accurate answers must await thorough research, based on other results (not shown) and anecdotal evidences we believe that the rise in the popularity of VIX ETNs, and the resulting exponential increase in short interest, has contributed greatly to the increase in the volatility of volatility.

We also note that from the Table above, out of the 11 occurrences, more than half (6 to be precise) happened after 2010, i.e. after the introduction of VIX ETNs.

With an increase in volatility of volatility, risk management became more critical, especially if you are net short volatility and/or you have a lot of exposure to the skew (dGamma/dSpot).

Using a Market Timing Rule to Size an Option Position

Position sizing and portfolio allocation have not received much attention in the options trading community. In this post we are going to apply a simple position sizing rule and see how it performs within the context of volatility trading.

An option position can be sized by using, for example, a Markov Model  where the size of the position can be a function of the regime transition probability [1]. While this is a research venue that we would like to explore, we decided to start with a simpler approach. We chose an algorithm that is intuitive enough for both quant and non-quant portfolio managers and traders.

We utilize the market timing rule proposed by Faber [2] who applied it to different asset classes in the context of portfolio allocation. The rule is as follows

Buy when monthly price > 10M SMA (10 Month Simple Moving Average)

Sell and move to cash when monthly price < 10M SMA

This remarkably simple timing rule has been used successfully by Faber and others.  It has proved to significantly improve portfolios’ risk-adjusted returns [3].

Within the context of volatility trading, we compare 2 option strategies

1-NoTiming: Sell 1-Month  at-the-money  (ATM) put option on every option expiration Friday.  The option is held  until maturity, i.e. for a month.  The position is kept delta neutral, i.e. it is rehedged at the end of every day.

2-10M-SMA: Similar to the above except that Faber’s timing rule is applied, i.e. we only sell an ATM put option if the closing price of the underlying is greater than its 10M SMA. Note, however, that unlike Faber,  here we define the end of month as the option expiration Friday, and not the calendar end of month.

A short discussion on the rationale for choosing a market timing rule is in order here. Within the context of portfolio allocation, the 10M SMA rule is used for timing the direction of the market, i.e. the PnL driver is mostly market beta. Our trade’s PnL driver is, on the other hand,  the dynamics  of the implied/realized volatility spread. But as shown in a previous post, the IV/RV volatility dynamics correlates highly with the market returns.  Therefore, we thought that we could use a directional timing strategy to size an options portfolio despite the fact that their PnL drivers are different, at least theoretically.

We tested the 2 strategies on SPY options from February 2007 to November 2016. Table below provides a summary of the trade statistics (average PnLs, winning/losing trades and drawdowns are in dollar).

Strategy NoTiming 10M-SMA
Number of Trades 115 81
Percent Winners 0.68 0.69
Average P&L 18.84 14.87
Largest losing trade -269.79 -248.50
Largest winning trade 243.54 154.22
Profit Factor (W/L)            1.77            1.64
Worst drawdown -633.24 -339.91

Graph below shows the equity curves of the 2 strategies

As it is observed from the Table and the Graph, except for the worst drawdown, we don’t see much of an improvement when the 10M-SMA timing rule is applied.  Although the 10M-SMA strategy avoided the worst period of the Global Financial Crisis, overall it made less money than the NoTiming strategy.

The non-improvement of Faber’s rule in the context  of volatility selling probably relates to the fact that we are using a directional timing algorithm to size a trade whose PnL driver  is the volatility dynamics . A position sizing algorithm based directly on the volatility dynamics would have a better chance  of success.  We are currently extending our research in this direction;  any comment, feedback is welcome.

 

References:

[1]  C. Donninger, Timing the Tail-Risk-Protection of the SPY with VIX-Futures by a Hidden Markov Model. The Wool-Milk-Sow Strategy. April 2017, http://www.godotfinance.com/pdf/TailRiskProtectionHMM.pdf

[2]  M. Faber, A  Quantitative  Approach  to  Tactical  Asset  Allocation, Journal  of Investing , 16, 69-79, 2007

[3] See for example A. Clare, J. Seaton, P. Smith and S. Thomas, The Trend is Our Friend: Risk Parity, Momentum and Trend Following in Global Asset Allocation, Aug 2012, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2126478

 

 

Is There a Less Expensive Hedge Than a Protective Put ?

The spot VIX index finished last Friday at 11.28, a relatively low number, while the SKEW index was making a new high. The SKEW index is a good proxy for the cost of insurance and right now it appears to be expensive. A high reading of SKEW means investors are buying out of the money puts for protection.

CBOE SKEW index as at close of March 17, 2017. Source: Barchart.com

With the cost of insurance so high, is there a less expensive way for investors to hedge their portfolios?

One might think immediately of cross-asset hedging. However, if we use other underlying to hedge, we will then take on correlation (basis) risk and if not managed correctly, it can add risks to the portfolio instead of protecting it.

In this post we examine different hedging strategies using instruments on the same underlying.  Our goal is to investigate the cost, risk/reward characteristics of each hedging strategy. Knowing the risk/reward profiles will allow us to design a cost-effective portfolio-protection scheme.

We will use Monte Carlo (MC) simulation to accomplish our goal [1]. The parameters and assumptions of the MC simulation are as follows:

Parameter Value
Initial stock price 100
Volatility 20%
Risk-free rate 0.02
Drift 0.07
Days in simulation 252
Time step (day) 1
Number of paths 10000
Model GBM [2]

 

The hedging strategies we’re investigating are:

1-NO HEDGE: no hedging is performed. The asset is allowed to evolve freely in a risky world. This would correspond to the portfolio of a Buy and Hold investor.

2-PPUT: protective put. We buy an at the money (ATM) put in order to hedge the downside. This strategy is the most common type of portfolio insurance.

3-GAMMA: convexity hedge.  We buy an ATM put, but we then dynamically hedge it. This means that we flatten out the delta at the end of every day.

The GAMMA hedging strategy is not used frequently in the industry. The rationale for introducing it here is that given a high price of a put option, we will try to partially recoup its cost by actively scalping gamma, while we still benefit from the positive convexity of the option. This means that in case of a market correction, the gamma will manufacture negative delta so that the hedging position can offset some of the loss in the equity portfolio.

We use 10000 paths in our MC simulation. At the end of 1 year, we calculate the returns (using a Reg-T account) and determine its mean and variance. We also calculate the Value at Risk at 95% confidence interval. The graph below shows the histogram of the returns for the NO HEDGE strategy,

Return histogram for the NO HEDGE strategy

Table below presents the expected returns, standard deviations and Value at Risks for the hedging strategies.

Strategies Expected return Standard Deviation Value at Risk
NO HEDGE 0.075 0.048 0.318
PPUT 0.052 0.024 0.118
GAMMA 0.066 0.029 0.248

 

As it is observed from the table, hedging with a protective put (PPUT) reduces the risks. Standard deviation and VaR are reduced from 0.048 and 0.318 to 0.024 to 0.118 respectively. However, the expected return is also reduced, from 0.075 to 0.052. This reduction is the cost of the insurance.

Interestingly, hedging using gamma convexity (GAMMA strategy) provides some reduction in risks (Standard deviation of 0.029, and VaR of 0.248), while not diminishing the returns greatly (expected return of 0.066).

In summary, GAMMA hedging is a strategy that is worth considering when designing a portfolio insurance scheme. It’s a good alternative to the often used protective (and expensive) put strategy.

 

Footnotes

[1] We note that the simulations were performed under idealistic assumptions, some are advantageous, and some are disadvantageous compared to a real life situation. However, results and the conclusion are consistent with our real world experience.

[2] GBM stands for Geometric Brownian Motion.

 

Forward Volatility and VIX Futures

Last week the VIX index was more or less flat, the contango was favorable, and yet VIX ETF such as XIV, SVXY underperformed the market. In this post we will attempt to find an explanation.

As briefly mentioned in the footnotes of the blog post entitled “A Volatility Term Structure Based Trading Strategy”, VIX futures represent the (risk neutral) expectation values of the forward implied volatilities and not the spot VIX. The forward volatility is calculated as follows,

Using the above equation, and using the VIX index for σ0,t , VXV for σ0,T, we obtain the 1M-3M forward volatility as shown below.

1M-3M forward volatility from October 2016 to February 2017

Graph below shows the prices of VXX (green and red bars) and VIX April future (yellow line) for approximately the same period. Notice that their prices have increased since mid February, along with the forward volatility, while the spot VIX (not shown) has been more or less flat.

VXX (green and red bars) and VIX April future (yellow line) prices

If you define the basis as VIX futures price-spot VIX, then you will observe that last week this basis widened despite the fact that time to maturity shortened.

In summary, VIX futures and ETF traders should pay attention to forward volatilities, in addition to the spot VIX. Forward and spot volatilities often move together, but they diverge from time to time. The divergence is a source of risk as well as opportunity.

 

A Volatility Skew Based Trading Strategy

In previous blog posts, we explored the possibility of using various volatility indices in designing market timing systems for trading VIX-related ETFs.  The system logic relies mostly on the persistent risk premia in the options market. Recall that there are 3 major types of risk premium:

1-Implied/realized volatilities (IV/RV)

2-Term structure

3-Skew

A summary of the systems developed based on the first 2 risk premia was published in this post.

In this article, we will attempt to build a trading system based on the third type of risk premium: volatility skew. As a measure of the volatility skew, we use the CBOE SKEW index.

According to the CBOE website, the SKEW index is calculated as follows,

The CBOE SKEW Index (“SKEW”) is an index derived from the price of S&P 500 tail risk. Similar to VIX®, the price of S&P 500 tail risk is calculated from the prices of S&P 500 out-of-the-money options. SKEW typically ranges from 100 to 150. A SKEW value of 100 means that the perceived distribution of S&P 500 log-returns is normal, and the probability of outlier returns is therefore negligible. As SKEW rises above 100, the left tail of the S&P 500 distribution acquires more weight, and the probabilities of outlier returns become more significant. One can estimate these probabilities from the value of SKEW. Since an increase in perceived tail risk increases the relative demand for low strike puts, increases in SKEW also correspond to an overall steepening of the curve of implied volatilities, familiar to option traders as the “skew”.

Our system’s rules are as follows:

Buy (or Cover) VXX  if SKEW  >=  10D average of SKEW 

Sell (or Short) VXX  if SKEW  <  10D average of SKEW 

The table below summarizes important statistics of the trading system

Initial capital 10000
Ending capital 40877.91
Net Profit 30877.91
Net Profit % 308.78%
Exposure % 99.50%
Net Risk Adjusted Return % 310.34%
Annual Return % 19.56%
Risk Adjusted Return % 19.66%
Max. system % drawdown -76.00%
Number of trades 538
Winners 285 (52.97 %)

The graph below shows the equity line from February 2009 to December 2016

Portfolio equity for the volatility SKEW trading strategy

We observe that this system does not perform well as the other 2 systems [1]. A possible explanation for the weak performance is that VXX and other similar ETFs’ prices are affected more directly by the IV/RV relationship and the term structure than by the volatility skew. Hence using the volatility skew as a timing mechanism is not as accurate as other volatility indices.

In summary, the system based on the CBOE SKEW is not as robust as the VRP and RY systems. Therefore we will not add it to our existing portfolio of trading strategies.

Footnotes

[1]  We also tested various combinations of this system and results lead to the same conclusion.

Relationship Between the VIX and SP500 Revisited

A recent post on Bloomberg website entitled Rising VIX Paints Doubt on S&P 500 Rally pointed out an interesting observation:

While the S&P 500 Index rose to an all-time high for a second day, the advance was accompanied by a gain in an options-derived gauge of trader stress that usually moves in the opposite direction

The article refers to a well-known phenomenon that under normal market conditions, the VIX and SP500 indices are negatively correlated, i.e. they tend to move in the opposite direction. However, when the market is nervous or in a panic mode, the VIX/SP500 relationship can break down, and the indices start to move out of whack.

In this post we revisit the relationship between the SP500 and VIX indices and attempt to quantify their dislocation.  Knowing the SP500/VIX relationship and the frequency of dislocation will help options traders to better hedge their portfolios and ES/VX futures arbitrageurs to spot opportunities.

We first investigate the correlation between the SP500 daily returns and change in the VIX index [1]. The graph below depicts the daily changes in VIX as a function of SP500 daily returns from 1990 to 2016.

Volatility index and S&P500 index correaltion
Daily point change in VIX v.s. SP500 return

We observe that there is a high degree of correlation between the daily SP500 returns and daily changes in the VIX. We calculated the correlation and it is -0.79 [2].

We next attempt to quantify the SP500/VIX dislocation. To do so, we calculated the residuals. The graph below shows the residuals from January to December 2016.

residuals VIX/SP500 regression
Residuals of VIX/SP500

Under normal market conditions, the residuals are small, reflecting the fact that SPX and VIX are highly (and negatively) correlated, and they often move in lockstep. However, under a market stress or nervous condition, SPX and VIX can get out of line and the residuals become large.

We counted the percentage of occurrences where the absolute values of the residuals exceed 1% and 2% respectively. Table below summarizes the results

Threshold Percentage of Occurrences
1% 17.6%
2% 3.9%

We observe that the absolute values of SP500/VIX residuals exceed 1% about 17.6% of the time. This means that a delta-neutral options portfolio will experience a daily PnL fluctuation in the order of magnitude of 1 vega about 17% of the time, i.e. about 14 times per year.  The dislocation occurs not infrequently.

The Table also shows that divergence greater than 2% occurs less frequently, about 3.8% of the time. This year, 2% dislocation happened during the January selloff,  Brexit and the US presidential election.

Most of the time this kind of divergence is unpredictable. It can lead to a marked-to-market loss which can force the trader out of his position and realize the loss. So the key in managing an options portfolio is to construct positions such that if a divergence occurs, then the loss is limited and within the allowable limit.

 

Footnotes:

[1] We note that under different contexts, the percentage change in VIX can be used in a correlation study.  In this post, however, we choose to use the change in the VIX as measured by daily point difference. We do so because the change in VIX can be related directly to Vega PnL of an options portfolio.

[2]  The scope of this post is not to study the predictability of the linear regression model, but to estimate the frequency of SP500/VIX divergence.  Therefore, we applied linear regression to the whole data set from 1990 to 2016. For more accurate hedges, traders should use shorter time periods with frequent recalibration.